Lemma 4.1 (Carleman estimate, see [1]}) 
Let \({\bf x}_0\)  be a point in \(\mathbb {R}^d \setminus \overline{\Omega }\)  such that \(r({\bf x}) = |{\bf x}- {\bf x}_0| > 1\)  for all \({\bf x}\in \Omega \) .
Let \(b > \max _{{\bf x}\in \overline{\Omega }} r({\bf x})\)  be a fixed constant.
There exist positive constants \(\beta _0\)  depending only on \(b\) , \({\bf x}_0\) , \(\Omega \)  and \(d\)  such that
for all function \(v \in C^2(\overline{\Omega })\)  satisfying
\(v({\bf x}) = \partial _{\nu } v({\bf x}) = 0 \quad \mbox{for all } {\bf x}\in \partial \Omega ,\) 
